Data processing method, data processing apparatus and processing apparatus

ABSTRACT

The present invention is a data processing apparatus including a data input/output device for receiving data, a storage for storing the data received by the data input/output device, a data processing program storage for storing a data processing program that includes the steps of calculating, using a double exponential smoothing method, a first predicted value that is a predicted value of smoothed data and a second predicted value that is a predicted value of the gradient of the smoothed data, and calculating, using a double exponential smoothing method in which the second predicted value is set as input data, a third predicted value that is a predicted value of smoothed data and a fourth predicted value that is a predicted value of the gradient of the smoothed data, and a data calculation processing apparatus for performing the data processing under the data processing program.

BACKGROUND OF THE INVENTION

The present invention relates to a data processing method and a dataprocessing apparatus for processing a series of numerical data on atarget system (device, analyzed data, or the like).

Various models have been proposed as techniques for smoothing orpredicting a series of numerical data on a target system. In addition,aiming at grasping the state of a target system, differential processessuch as first differential and second differential of data arefrequently used so as to detect an extreme value (maximum value orminimum value) or an inflection point, which is a changing point in thedata. In particular, in the case of time series data such as measureddata containing noise and the like, a technical issue is to perform adata smoothing process and a differential process with high precision todetect a changing point in a target system, and to control the targetsystem.

Conventional techniques to perform data smoothing and data predictioninclude a curve fitting method, a moving average method, and the like,as described in K. Takahashi, “Inside Data Processing”, Journal ofSurface Analysis Vol. 7, No. 1, 2000, p. 68-p. 77. The curve fittingmethod includes a polynomial curve-fitting method (Savitzky-Golaymethod), as described in JP-A-2000-228397, and in addition, a digitalfilter includes a Butterworth low-pass filter. Furthermore, the movingaverage method includes an exponential smoothing method, and the like,as described in A. C. Harvey, “TIME SERIES MODELS”, translated by N.Kunitomo & T. Yamamoto, University of Tokyo Press, 1985, p. 173.Although “TIME SERIES MODELS” discloses a single exponential smoothingmethod (with one smoothing parameter), a double exponential smoothingmethod (with two smoothing parameters) is also used in economics-relatedfields such as supply and demand estimation.

For conventional techniques to perform a data differential process, afinite difference method is frequently used, as described in “FluidCalculation and Finite Difference Method” written and edited by K.Kuwahara & T. Kawamura, Asakura Publishing, 2005, p. 1. In addition, itis the case that a polynomial curve-fitting method (Savitzky-Golaymethod) is used therefor, as described in JP-A-2000-228397. Furthermore,as an example in which time series data such as measured data containingnoise and the like is subjected to a data smoothing process, a changingpoint of data is detected through a first differential process and asecond differential process, and a target system is controlled,JP-A-61-53728 discloses a method in a plasma etching processingapparatus that includes subjecting spectral intensity signal data basedon plasma emission to a data smoothing process by a moving averageprocess and determining the end point of etching process with a firstdifferential value and a second differential value.

As described in JP-A-2000-228397, when the data differential process isperformed by the finite difference method and if the data smoothingprocess is not sufficient, the output result of the first differentialprocess contains much noise, resulting in data being not smooth andhaving a low S/N ratio (ratio of signal/noise). When the datadifferential process is performed again by the finite difference methodusing the above data, the output result of the second differentialprocess contains still more noise, resulting in data being not smoothand having a further low S/N ratio, which is problematic.

When difference intervals are increased, the output result of the firstdifferential process and the output result of the second differentialprocess are obtained as smooth data and have an increased S/N ratio(note that there is an optimal value for the difference interval), butin the case of the time series data, in particular, there is a problemthat the amount of data delay caused by the data differential processincreases. In addition, in a low-pass filter, or the like, when acut-off frequency is decreased, the output data of the firstdifferential process and the output data of the second differentialprocess are obtained as smooth data and have an increased S/N ratio(note that there is an optimal value for the cut-off frequency), but aswith the above, there is a problem in that the amount of data delaycaused by the data differential process increases.

Furthermore, in the case where the data differential process isperformed using a polynomial curve-fitting method (Savitzky-Golaymethod), a plurality of pieces of data are generally needed and adifferential value is derived at a point in time of the middle piece ofthe data. For this reason, there is a problem with the sequential dataprocessing that a time delay occurs in principal by at least a timedifference between a point in time of the latest piece of the data andthe point in time of the middle piece of the data.

Furthermore, in the data smoothing process, errors tend to develop ingeneral during a certain period of time immediately after the start ofthe data processing. For example, in the case of the time series data,the data period is short and a sampling time interval is long, and thusif the number of pieces of the data is small, a ratio of the periodduring which the error is large with respect to the whole data period islarge. In addition, there is a problem that performing the datadifferential process in the period during which the error is large haslittle reliability.

Furthermore, there is a method disclosed in JP-A-61-53728 as an endpoint determining method in the plasma etching in the plasma etchingprocessing apparatus, but the end point determining method in the plasmaetching disclosed in JP-A-61-53728 involves the following two problems.

Current semiconductor devices each have a high-step structure such as aFin Field Effect Transistor (Fin FET) structure due to higherperformance and integration. In addition, in normal plasma etching,microloading occurs, which is the difference in etching performancebetween sparse patterns and dense patterns. Furthermore, a thickness offilm to be etched is not uniform across the surface of a wafer.

For these reasons, for example, there is the case where time series dataon spectral intensity signal data based on plasma emission used fordetermining the end point of plasma etching changes in two stages.Hence, in the case where the time series data on the spectral intensitysignal data based on the plasma emission changes in two stages, and theend point of the plasma etching is determined at the second change, dataprocessing cannot track the second change and the end point of theplasma etching cannot be detected because the first change and thesecond change occur in a short time. Note that, here, a point in time atwhich the time series data on the spectral intensity signal data basedon the plasma emission changes is defined as the end point of the plasmaetching.

Furthermore, for example, in a plasma etching the period of which isshort with respect to retardation times of a first differential valueand a second differential value, in case where the end point of plasmaetching is determined by the change of the time series data on thespectral intensity signal data based on the plasma emission, dataprocessing to calculate the first differential value or the seconddifferential value cannot track a change, to be the end point of plasmaetching, in time series data on spectral intensity signal data based onplasma emission. That is, the responsiveness of detecting the end pointof plasma etching process is insufficient, which is the first problem.

Next, mask patterns for plasma etching are roughly divided into groovepatterns and hole patterns. In addition, an aperture ratio of a wafer ofa hole pattern is normally less than an aperture ratio of a wafer of agroove pattern, and there is even a case where the aperture ratio isless than 1%. Furthermore, the spectral intensity of plasma emission isreduced as the aperture ratio becomes small. For this reason, forexample, in the case of a wafer of an aperture ratio of less than 1%, itis difficult to detect the end point of plasma etching process since achange in the time series data on the spectral intensity signal databased on the plasma emission is too small. That is, a low S/N ratiocannot be supported, which is the second problem. Note that, here, theaperture ratio is a ratio of an area to be etched to the entire area ofthe wafer.

For the foregoing reasons, in the case of detecting a changing point ina target system with first differential data or second differential dataand controlling the target system, there is a problem that the precisionof the control is insufficient due to a low S/N ratio and a time delay,or the like.

SUMMARY OF THE INVENTION

In view of this, the present invention provides a data processing methodand a data processing apparatus that achieve both a high S/N ratio and areduced data delay in a data processing method and a data processingapparatus for processing data.

The present invention is a data processing apparatus including a datainput/output device which is configured to receive data to be processed,a storage which is configured to store the data received by the datainput/output device, a data processing program storage which isconfigured to store a data processing program that includes the steps ofcalculating, using a double exponential smoothing method, a firstpredicted value that is a predicted value of smoothed data and a secondpredicted value that is a predicted value of the gradient of thesmoothed data, and calculating, using a double exponential smoothingmethod in which the second predicted value is set as input data, a thirdpredicted value that is a predicted value of smoothed data and a fourthpredicted value that is a predicted value of the gradient of thesmoothed data, and a data calculation processing apparatus which isconfigured to perform the data processing under the data processingprogram, wherein the data input/output device outputs the firstpredicted value calculated by the data calculation processing apparatusas the result of a data smoothing process, a second predicted valuecalculated by the data calculation processing apparatus or a thirdpredicted value calculated by the data calculation processing apparatusas the result of a first differential process, and a fourth predictedvalue calculated by the data calculation processing apparatus as theresult of a second differential process, respectively.

The present invention is a processing apparatus including a processingchamber to be a control object, a measuring device which is configuredto obtain data relating to the processing chamber, a data calculationprocessing apparatus which is configured to perform data processingunder a data processing program that includes the steps of calculating,using a double exponential smoothing method, a first predicted valuethat is a predicted value of smoothed data, a second predicted valuethat is a predicted value of the gradient of the smoothed data, andcalculating, using a double exponential smoothing method in which thesecond predicted value is set as input data, a third predicted valuethat is a predicted value of smoothed data and a fourth predicted valuethat is predicted value of the gradient of the smoothed data, and acontroller which is configured to detect the state of the processingchamber or a change in the state of the processing chamber on the basisof at least one of the first predicted value calculated by the datacalculation processing apparatus, the second predicted value calculatedby the data calculation processing apparatus, the third predicted valuecalculated by the data calculation processing apparatus, and the fourthpredicted value calculated by the data calculation processing apparatus,and to control the processing chamber according to the detection result.

The present invention is a processing apparatus including a processingchamber to be a control object, a measuring device which is configuredto obtain data relating to the processing chamber, a data calculationprocessing apparatus which is configured to perform data processingunder a data processing program that uses a responsive doubleexponential smoothing method in which smoothing parameters are varied inaccordance with an error between the data obtained by the measuringdevice and the predicted value of smoothed data, and that processes datawhile making a lower limit value of the variable range of the smoothingparameters greater than zero, and a controller which is configured todetect the state of the processing chamber or a change in the state ofthe processing chamber on the basis of at least one of the result of adata smoothing process calculated by the data calculation processingapparatus, the result of a first differential process calculated by thedata calculation processing apparatus, and the result of a seconddifferential process calculated by the data calculation processingapparatus, and to control the processing chamber according to thedetection result.

The present invention is a processing apparatus including a processingchamber in which a sample mounted on a sample stage is subjected to aplasma process, a measuring device which is configured to obtain lightemission data in the plasma process of the sample, a data calculationprocessing apparatus which is configured to perform data processingunder a data processing program that uses a responsive doubleexponential smoothing method in which smoothing parameters are varied inaccordance with an error between the data obtained by the measuringdevice and the predicted value of smoothed data, and that processes datawhile making a lower limit value of the variable range of the smoothingparameters greater than zero, a controller which is configured to detecta plasma processing state of the sample or a change in the plasmaprocessing state of the sample on the basis of at least one of theresult of data smoothing process calculated by the data calculationprocessing apparatus, the result of a first differential processcalculated by the data calculation processing apparatus, or the resultof a second differential process calculated by the data calculationprocessing apparatus, and to control the processing chamber according tothe detection result.

The present invention is a data processing method for processing datausing a double exponential smoothing method, including the steps ofcalculating, using the double exponential smoothing method, a firstpredicted value that is a predicted value of smoothed data and a secondpredicted value that is a predicted value of the gradient of smootheddata, and calculating, using a double exponential smoothing method inwhich the second predicted value is set as input data, a third predictedvalue that is a predicted value of smoothed data and a fourth predictedvalue that is a predicted value of the gradient of smoothed data.

The present invention is a data processing method for processing datausing a double exponential smoothing method including the steps ofcalculating an approximate polynomial of an arbitrary number of piecesof data immediately following the start of data input, calculating,using the approximate polynomial, a first predicted value that is apredicted value of smoothed data immediately preceding the start of datainput, calculating a second predicted value that is a predicted value ofthe gradient of the smoothed data immediately preceding the start ofdata input, and subjecting the data to a double exponential smoothingprocess as the first predicted value and the second predicted value areset as initial values.

The present invention is a data processing method for processing datausing a responsive double exponential smoothing method in whichsmoothing parameters are varied in accordance with the error between theinput data and the predicted value of smoothed data, wherein a lowerlimit value of the variable range of the smoothing parameters is greaterthan zero.

The present invention is a data processing method for processing datausing an exponential smoothing method, wherein when N denotes a naturalnumber, the exponential smoothing method is an N-tuple exponentialsmoothing process to perform a data smoothing process on the data andperform the first to (N−1)th smoothing processes to gradient of thedata.

The present invention is a plasma processing method for subjecting asample to a plasma process, including processing, using a responsivedouble exponential smoothing method in which light emission data in theplasma process of the sample is measured and smoothing parameters arevaried in accordance with the error between the measured light emissiondata and the predicted value of smoothed light emission data, the lightemission data while making a lower limit value of the variable range ofthe smoothing parameters greater than zero, detecting the plasmaprocessing state of the sample or a change in the plasma processingstate of the sample on the basis of at least one of the result of a datasmoothing process calculated by the responsive double exponentialsmoothing method, the result of a first differential process calculatedby the responsive double exponential smoothing method, and the result ofa second differential process calculated by the responsive doubleexponential smoothing method, and controlling the plasma process of thesample according to the detection result.

According to the present invention, a high S/N ratio and a reduced datadelay are both achieved in a data processing method and a dataprocessing apparatus for processing data.

Other objects, features and advantages of the invention will becomeapparent from the following description of the embodiments of theinvention taken in conjunction with the accompanying drawings.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a diagram showing the entire configuration of a dataprocessing apparatus 1 according to a first embodiment;

FIG. 2 is a diagram showing the flow of data processing according to thefirst embodiment;

FIG. 3 is a diagram showing the flow of deriving an initial value in thefirst embodiment;

FIG. 4 is a vertical cross sectional view of an electron cyclotronresonance microwave plasma etching system according to the firstembodiment;

FIG. 5 is a flowchart of typical data processing of detecting the endpoint of etching process;

FIGS. 6A-C show the results of data processing by the data processingapparatus of the first embodiment;

FIGS. 7A-C are the data processing results of data smoothing and a datadifferential process with a conventional low-pass filter and by finitedifference method;

FIG. 8 is a diagram showing a relation between a response coefficientand the absolute value of relative error/absolute error in a secondembodiment when an exponentiation N is used as a parameter;

FIGS. 9A-C are graphs showing the data processing results when theexponential parameter N=1 in a data processing apparatus of the secondembodiment;

FIGS. 10A-C are graphs showing the data processing results when theexponential parameter N=5 in the data processing apparatus of the secondembodiment;

FIGS. 11A-C are graphs showing the data processing results in the casewhere a changing point of data follows immediately after the start ofdata input when the exponential parameter N=1 in the data processingapparatus of the second embodiment; and

FIG. 12 is a diagram showing the flow of data processing according to anembodiment 3.

DETAILED DESCRIPTION OF THE EMBODIMENTS

Embodiments of the present invention will be described below withreference to the drawings.

First Embodiment

A data processing apparatus according to a first embodiment of thepresent invention will be first described with reference to FIG. 1 toFIG. 7. Here, an example will be described in which the presentinvention is applied to the detection of an end point of etching processusing plasma emission spectrography aiming at a high-precision etchingprocess in an electron cyclotron resonance microwave plasma etchingsystem.

FIG. 1 shows a configuration diagram of a data processing apparatus 1 ofthe first embodiment. In the present embodiment, the data processingapparatus 1 is configured by a data input/output device 2, a datastorage 3 being a storage, a data processing program storage 4, and adata calculation processing apparatus 5, which are connected to oneanother so as to exchange data. In addition to the above, a data display(not shown) is further provided as needed. The data processing apparatus1 can perform input/output of data with a target system 6 (device,analyzed data, or the like). The data processing apparatus 1 therebycontrols the target system 6 with high precision. In the case of thepresent embodiment, the target system 6 is a microwave plasma processingsystem. Furthermore, the data processing apparatus 1 may be usedstandalone and can be used for data analysis or the like.

The data input/output device 2 can input/output processed data orparameters of a data processing program. The data input/output device 2receives data to be processed collectively or sequentially, from thetarget system 6 or the like, stores the data in the data storage 3 suchas a RAM, subjects the data to a data smoothing process and a datadifferential process using the data calculation processing apparatus 5according to the data processing program stored in the data processingprogram storage 4 such as a RAM, and outputs the result data on the datasmoothing process and the result data on the data differential processto the target system 6 or the like using data input/output device 2,which are used for controlling the target system 6.

FIG. 2 shows the total flow of a data processing method stored in thedata processing program. The data to be processed collectively orsequentially is received and input. In the present embodiment, the inputdata is defined as time series data Y1_(t): t=1, 2, . . . . Next,initial values are derived according to a method to be describedhereafter. Next, a first-time double exponential smoothing process isperformed by the following expressions (1) and (2), and a predictedvalue S1_(t) of data smoothing and a predicted value B1_(t) of thegradient of smoothed data of the first output are obtained.Data smoothing: S1_(t)=α1Y _(t)+(1−α1)(S1_(t-1) +B1_(t-1))  Expression(1)Gradient of the smoothed data:B1_(t)=γ1(S1−S1_(t-1))+(1−γ1)B1_(t-1)  Expression (2)

Next, a second-time double exponential smoothing process is performed,in which the predicted value B1_(t) of the gradient of the smoothed datain the first output is set as a second input data Y2_(t), and apredicted value S2_(t) of data smoothing and a predicted value B2_(t) ofthe gradient of smoothed data of the second output are obtained. Next,result data on the data smoothing process S1_(t), result data on a firstdifferential data process S2_(t), and result data on second differentialdata processing B2_(t) are output collectively or sequentially. Here, asmoothing parameter α1 of the data smoothing and a smoothing parameterγ1 of the gradient of the smoothed data in the first-time doubleexponential smoothing, and a smoothing parameter α2 of the datasmoothing and a smoothing parameter γ2 of the gradient of the smootheddata in a second-time double exponential smoothing are set at arbitraryconstants in advance.

Note that 0<α1<1, 0<γ1<1, 0<α2<1, and 0<γ2<1. The predicted value B1_(t)of the gradient of the smoothed data of the first output may be usedsince it is equivalent to the processing result of the firstdifferential, but the data result varies widely, and thus a datasmoothing process is performed by the second-time double exponentialsmoothing process.

FIG. 3 shows a flowchart of deriving the initial values in the presentembodiment. The initial value of the predicted value S1 of the datasmoothing and the initial value of the predicted value B1 of thegradient of the smoothed data in the double exponential smoothingprocess are typically derived by, for example, the following method. Theinitial value of the predicted value S1 of the data smoothing is derivedby S1=input data Y1 (method A1), or S1=the average value ({Y1+Y2+ . . .+YN}/N) of the number of initial pieces of the input data (method A2),or the like. The initial value of the predicted value B1 of the gradientof the smoothed data is derived by B1=Y2−Y1 (method B1),B2={(Y2−Y1)+(Y4−Y3)}/2 (method B2), or the like.

In general, there has been a problem with the double exponentialsmoothing process of developing a large error immediately after thestart of the data processing. One of the causes thereof is that initialvalues by the above conventional method of deriving have large errorswith respect to a predicted value of data smoothing to initial pieces ofactual data and a predicted value of the gradient of smoothed data onthe initial pieces of actual data, respectively. In addition, inconventional methods, initial values are derived using the desirednumber N of initial pieces of data and (N+1)th and subsequent pieces ofthe input data of Y_(N+1), . . . are thereafter subjected to the doubleexponential smoothing process, but the number N of initial pieces of theinput data are not subjected to the double exponential smoothingprocess, which results in the lack of data output results correspondingto the above period.

In particular, if the number of pieces of input data to be processed issmall, the effect of the lack of the above data output result becomesprominent. For the above reasons, there has been a problem that, if thestate of a target system changes immediately after the beginning of thedata, it is difficult to control the target system with high precisiondue to the large errors in the data processing immediately after thestart of the data processing, or the lack of the data output resultimmediately after the beginning of the data.

As shown in FIG. 3, in the present embodiment, an approximate polynomialis derived by the least squares method using the desired number N ofinitial pieces of data Y1_(t) (t=1, 2, . . . , N) after the start of thedata input. In the present embodiment, ten pieces of time series datawith isochronous intervals are used. With the approximate polynomialderived in the above, a predicted value S1₀ of data smoothing, which isvirtual data at t=0 immediately preceding the input data, and thepredicted value B1₀ of the gradient of the smoothed data are derived. Inthe present embodiment, a linear function is used as the approximatepolynomial, and the predicted value S1₀ of the data smoothing, and thepredicted value B1₀ of the gradient of the smoothed data are calculatedby Expressions (3) and (4), respectively.The predicted value S1₀ of the datasmoothing={330Y1₁+275Y1₂+220Y1₃+165Y1₄+110Y1₅+55Y1₆+0Y1₇−55Y1₈−110Y1₉−165Y1₁₀}/825  Expression(3)The predicted value B1₀ of the gradient of the smootheddata={−45Y1₁−35Y1₂−25Y1₃−15Y1₄−5Y1₅+5Y1₆+15Y1₇+25Y1₈+35Y1₉+45Y1₁₀}/825  Expression(4)

In addition, an initial value S2₁ of the predicted value of the datasmoothing and an initial value B2₁ of the predicted value of thegradient of the smoothed data, in the second-time double exponentialsmoothing process shown in FIG. 2, are set at S2₁=S1₁, and B2₁=0,respectively. In the case of sequential data processing, the initialvalues are derived after inputting the number N of initial pieces of thedata, and thereafter the number N of initial pieces of the data aresequentially subjected to the double exponential smoothing process, andthe results of the data smoothing process and the data differentialprocess are output. Thereafter (subsequent to t=N+1), the doubleexponential smoothing process is sequentially performed every input of apiece of the data, and the results of the data smoothing process and thedata differential process are output in real time. For this reason,according to the present embodiment, there is an advantage of performingthe data smoothing process and the data differential process with smallerrors and high precision even to the initial pieces of the input dataafter the start of the data input.

FIG. 4 shows a vertical cross sectional view of an electron cyclotronresonance microwave plasma etching system according to the firstembodiment of the present invention. In the present embodiment theelectron cyclotron resonance microwave plasma etching system correspondsto the target system 6 (device, analyzed data, or the like) of FIG. 1. Avacuum pumping apparatus 13 decompresses the inside of a processingchamber 11, which is defined by a container 7, a discharge tube 8, aquartz plate 9, and a quartz window 10, by opening an exhaust valve 12.Etching gas passes though gas piping 14 via a mass flow controller (notshown), passes through between the quartz plate 9 and a quartz showerplate 15, and is led into the processing chamber 11 through the gasholes of the quartz shower plate 15. The pressure of the etching gas ledinto the processing chamber 11 is adjusted to a desired pressure by apump speed control valve 16.

In addition, the processing chamber 11 is in a magnetic field generatedby coils 17 and 18 and a yoke 19. Microwaves having a frequency of 2.45GHz in this case oscillated by a magnetron 20 propagate through arectangular waveguide 22 via an isolator (not shown), a power monitor(not shown), a matching box 21, in a rectangular TE10 mode, andpropagate through a circular waveguide 24 via a rectangular-to-circularmode converter 23, in a circular TE11 mode. The microwaves arethereafter led into a cavity resonator 25, and penetrate through thequartz plate 9 and the quartz shower plate 15 to enter into theprocessing chamber 11. A magnetic field region having a magnetic fluxdensity of 875 Gauss that produces electron cyclotron resonance with theled microwaves of 2.45 GHz is formed all over the processing chamber 11in a direction perpendicular to the central axis of the processingchamber 11 and to a direction of leading the microwaves, and in across-sectional direction with respect to the central axis of theprocessing chamber 11.

With plasma produced mainly by the interaction between the microwaves of2.45 GHz and the magnetic field of 875 Gauss, a wafer 27 placed on awafer mounting electrode 26 being a sample stage (holder) is subjectedto an etching process. In addition, a radio frequency power source 28 isconnected to the wafer mounting electrode 26 via the matching box (notshown) in order to control the etch profile of the wafer 27 being asample, which allows radio frequency voltage to be applied. Furthermore,a chiller unit (not shown) is connected to the wafer mounting electrode26, which allows the temperature of the wafer 27 to be controlled.

The processing chamber 11, the wafer 27, and the wafer mountingelectrode 26 are disposed coaxially, and a gas hole region of the quartzshower plate 15 for leading the etching gas, the exhaust valve 12 beingan evacuating section, the pump speed control valve 16, and the vacuumpumping apparatus 13 are also disposed coaxially with respect to theprocessing chamber 11. Thus, the flow of gas above the wafer 27 iscoaxial and symmetrical. The coils 17 and 18, and the yoke 19 forproducing the magnetic field are also disposed coaxial with respect tothe processing chamber 11, and thus a magnetic field profile in theprocessing chamber 11 and an electron cyclotron resonance region havinga magnetic flux density of 875 Gauss are formed coaxial with respect tothe processing chamber 11. In addition, the circular waveguide 24 andthe cavity resonator 25 are also disposed coaxially with respect to theprocessing chamber 11, and thus the microwaves led into the processingchamber 11 are also led coaxially with respect to the processing chamber11.

Since the magnetic field is formed coaxially with respect to theprocessing chamber 11 and the microwaves are led coaxially with respectto the processing chamber 11, the plasma produced by the interactionbetween the magnetic field and the microwaves is produced coaxially withrespect to the processing chamber 11, and electrons and ions in theplasma are transported coaxially with respect to the wafer 27. Inaddition, since the flow of the etching gas is coaxial with respect tothe processing chamber 11, radicals produced by the plasma or thebyproducts produced by etching the wafer 27 are also led and exhaustedcoaxially with respect to the wafer 27. As a result, it is possible toperform etching process with etching process performances such as anetching rate, a material selectivity, and an etch profile well uniformedacross the surface of the wafer.

Light from the plasma produced in the processing chamber 11 through alateral side of the processing chamber 11 is led into a spectroscope 30via the quartz window 10 and an optical fiber 29, and is output aswavelength-dependent time series data on the intensity of the light. Inaddition, light through the upper side of the processing chamber 11 isled into a spectroscope 32 via the quartz shower plate 15, the quartzplate 9, the cavity resonator 25, the circular waveguide 24, therectangular-to-circular mode converter 23, and an optical fiber 31, andoutput as wavelength-dependent time series data on the intensity of thelight.

Into the processing chamber 11, etching byproducts from the etching gasand the wafer 27 are led, and they are dissociated by the interactionbetween the microwave and the magnetic field to generate plasma. Forthis reason, the light from the plasma produced in the processingchamber 11 contains information on atoms, molecules, radicals, and thereactants thereof that compose the etching gas and the etchingbyproducts.

For example, in typical poly-Si etching of a Si substrate in which apoly-Si film and a SiO₂ film is disposed underneath a mask pattern, itis required to perform the poly-Si etching with a high selectivity to aSiO₂. A halogen-based gas is used as the etching gas, and the etchingbyproducts include a Si and a halogen, being a member to be etched. Theetching byproducts are dissociated by the plasma again, and thus thespectroscope 30 and the spectroscope 32 monitor the intensity of thelight emission having a wavelength of 288 nm that is originated from aSi from the plasma. In this case, when the etching of the poly-Si filmis completed and the SiO₂ is exposed, the intensity of the plasmaemission having the wavelength of 288 nm that is originated from a Sisharply lowers and finally approaches a certain value since the etchingrate of the SiO₂ is small. The changes in the plasma emission aremonitored to detect the end point of etching process.

The light through the lateral side of the processing chamber 11 containsthe information on the etching gas and the etching byproducts, and thelight through the upper side of the processing chamber 11 contains, inaddition to the information, information on the membrane structure andthe stepped structure of the wafer 27 because the interference of theplasma light occurs in the membrane structure and the stepped structureof the wafer 27. It is possible to monitor the thickness of film and thedepth of etching in the etching by analyzing data on the plasmaemission. In the present embodiment, for ease of description, data onthe plasma emission through the lateral side of the processing chamber11 is used for monitoring the end point of etching process.

FIG. 5 shows a typical data processing flow of detecting the end pointof etching process. Input data is created by an evaluation function ofExpression (5) that simulates changes in the intensity of plasmaemission in an etching.Y(t)=H/[1+exp{−A(t−T)}]+Ct+D+F(R−0.5)  Expression (5)

Here, H, A, T, C, D, and F are arbitrary constants, and R is a randomnumber ranging from 0 to 1. Using the evaluation function allows forcomparing and evaluating data processing performances in various methodsof data processing, such as absolute errors with respect to actualvalues, a retardation time associated with the data processing, and aS/N ratio (signal/noise), since analytic actual values in a datasmoothing process, a first differential process, and a seconddifferential process are known.

As shown in FIG. 5, in the typical data processing of detecting the endpoint of etching process, an input data waveform shown in the (A) ofFIG. 5 is subjected to a data smoothing process as shown in the (B) ofFIG. 5, and thereafter subjected to a first differential process asshown in the (C) of FIG. 5 and to a second differential process as shownin the (D) of FIG. 5. The data smoothing process clarifies a changingpoint in the input data containing much noise. The changing point isdetected as a point (point in time) at a peak value through the firstdifferential process, and detected as a point (point in time) at zerocrossing through the second differential process. With this as a basis,the end point of etching process is determined, and the etching deviceis thereby controlled to perform the etching process with highprecision.

The changing point becomes more clearly and simply determinable with thepeak through the first differential process and the zero crossingthrough the second differential process, gradually, but the absolutevalue of the intensity of signal gradually becomes small. For thisreason, data processing with a high S/N ratio is important. Inparticular, in the cases of etching in which area to be etched is smallor etching in which a mask pattern having a low aperture ratio is used,data processing with an even higher S/N ratio since the changes in theintensity of plasma emission across the end point of etching process issmall. In general, in the data smoothing process and the datadifferential process, a retardation time becomes longer as an S/N ratiobecomes high, which makes an absolute error with respect to an actualvalue large. That is, the relationship between the S/N ratio, and theretardation time and the absolute error is a tradeoff, and a datasmoothing process and a data differential process that simultaneouslysatisfy the S/N ratio, the retardation time, and the absolute error, areneeded.

In the present embodiment, the data processing shown in FIG. 5 isperformed using the flows of the data smoothing process and the datadifferential process of FIG. 2 and FIG. 3. In addition, the input dataof FIG. 5 is equivalent to the output data from the spectroscope 30 formonitoring the plasma emission in the etching in the electron cyclotronresonance microwave plasma etching system of FIG. 4. As shown in FIG. 4,a system controller 33 (including a data input/output device, a dataprocessing apparatus, and a data display) for controlling the electroncyclotron resonance microwave plasma etching system as a system, and thedata processing apparatus 1 of the present embodiment are provided. Thedata processing apparatus 1 may be incorporated as part of the systemcontroller 33.

The output data from the spectroscope 30 and the spectroscope 32 istransmitted to the data processing apparatus 1, and the result of datasmoothing process, the result of first data differential, and the resultof second data differential are transmitted to the system controller 33being a controller. The system controller 33 determines the end point ofetching process on the basis of the result of data smoothing process,the result of first data differential, and the result of second datadifferential, and controls the electron cyclotron resonance microwaveplasma etching system as a system. In FIG. 4, connection between thesystem controller 33, and the magnetron 20 and the radio frequency powersource 28 is shown because, in the determination of the end point ofetching process, plasma production is mainly controlled. In addition,the system controller 33 is connected to other devices configuring thesystem, the illustrations of which are omitted in FIG. 4.

FIGS. 6A-C show the results of the data processing by the dataprocessing apparatus 1 of the first embodiment of the present invention.FIG. 6A shows input data and a waveform after the data smoothingprocess, FIG. 6B shows a waveform after the first differential process,and FIG. 6C shows a waveform after the second differential process. Inaddition, FIGS. 7A-C show the results of data processing performed bythe data processing apparatus 1 using a low-pass filter and a finitedifference method of prior art. In this case, a cut-off frequency of thelow-pass filter is set at 0.025 Hz, FIG. 7A shows input data and awaveform after data smoothing process, FIG. 7B shows a waveform after afirst differential process, and FIG. 7C shows a waveform after a seconddifferential process. Here, the pieces of input data used for FIGS. 6A-Cand FIGS. 7A-C are the same.

As compared between FIGS. 6A-C and FIGS. 7A-C, as shown in FIG. 6A, withthe data smoothing process and data differential process device of thefirst embodiment of the present invention, the absolute errors betweenthe input data and the result of data smoothing process are very small,and it can be understood that the data smoothing process is preferablyperformed. In addition, as shown in FIG. 6B and FIG. 6C, the firstdifferential process and the second differential process can beperformed with high S/N ratios. For this reason, it is possible toclearly detect the point (point in time) at a peak in the firstdifferential and a point (point in time) at zero crossing in the seconddifferential, which are criteria for determining the end point ofetching process. Comparing data processing performances using numericaldata, the above absolute error is 22.4 by the data smoothing process andthe data differential process device of the first embodiment of thepresent invention, whereas being 191.2 by the low-pass filter and thefinite difference method of prior art.

Furthermore, the S/N ratio is 32 by the data smoothing process and thedata differential process device of the first embodiment of the presentinvention, whereas being 28 by the low-pass filter and the finitedifference method of prior art. The zero crossing time point in thesecond differential by the data smoothing process and the datadifferential process device of the first embodiment of the presentinvention is earlier by 5.4 seconds than that by the low-pass filter andthe finite difference method of prior art, which means that theretardation time is short.

According to the first embodiment of the present invention, there is anadvantage of consecutively performing the data smoothing process and thedata differential process with a small error of absolute value, a highS/N ratio, and a short retardation time, in real time.

Second Embodiment

A data processing apparatus according to a second embodiment of thepresent invention will be next described. In the present embodiment,Expressions (1) and (2) of the first-time double exponential smoothingprocess, in FIG. 2 showing the total flow of the method of the datasmoothing process and the data differential process in the firstembodiment of the present invention, are replaced with the followingExpressions (6) to (15).Data smoothing: S1_(t)=α1_(t) Y _(t)+(1−α1_(t))(S1_(t-1)+B1_(t-1))  Expression (6)Gradient of the smoothed data: B1_(t)=γ1_(t)(S1_(t)−S1_(t-1))+(1−γ1_(t))B1_(t-1)  Expression (7)Smoothing parameter: α1_(t)=(K _(α) −L _(α))F _(α) +L _(α)  Expression(8)Response coefficient: F _(α)=(|δα_(t)/Δα_(t)|+φ)^(N)  Expression (9)Relative error: δα_(t) =A1(Y _(t) −S1_(t))+(1−A1)δα_(t-1)  Expression(10)Absolute error: Δα_(t) =A1|Y _(t) −S1_(t)|+(1−A1)Δα_(t-1)+φ  Expression(11)Smoothing parameter: γ1_(t)=(K _(γ) −L _(γ))F _(γ) +L _(γ)  Expression(12)Response coefficient: F _(γ)=(|δγ_(t)/Δγ_(t)|+φ)^(N)  Expression (13)Relative error: δγ_(t) =A2{(S1_(t) −S1_(t-1))−B_(t)}+(1−A2)δγ_(t-1)  Expression (14)Absolute error: Δγ_(t) =A2|(S1_(t) −S1_(t-1))−B_(t)|+(1−A2)Δγ_(t-1)+φ  Expression (15)

Here, K_(α), L_(α), K_(γ), L_(γ), N, A1, A2, and φ are arbitraryconstants. Note that 1>K_(α)>L_(α)>0, 1>K_(γ)>L_(γ)>0, 1>A1>0, and1>A2>0. The constant φ is provided for preventing the absolute errorsΔα_(t) and Δγ_(t), and the response coefficients F_(α) and F_(γ) frombecoming zero, and an infinitesimal value are selected therefor so as tosignificantly lessen effects on normal calculations.

Expression (6) of the data smoothing and Expression (7) of the gradientof the smoothed data have forms basically same as those in the case ofthe first embodiment of the present invention of FIG. 2, but as shown inExpression (8) and Expression (12), the smoothing parameter α1_(t)sequentially varies within the range of K_(α)>α1_(t)>L_(α), and thesmoothing parameter γ1_(t) sequentially varies within the range ofK_(γ)>γ1_(t)>L_(γ), according to the state of the data processing. Inaddition, as shown in Expression (9) and Expression (13), the responsecoefficient F_(α) is an exponential response to the absolute value ofthe relative error/absolute error of the data smoothing, and theresponse coefficient F_(γ) is an exponential response to the absolutevalue of the relative error/absolute error of the gradient of thesmoothed data. Expression (10), Expression (11), Expression (14), andExpression (15) perform accumulation and smoothing such that recentpieces of data have greater effects and past pieces data haveexponentially reduced effects, and constants A1 and A2 are parametersfor performing an exponential accumulation and smoothing.

Expression (10) for the relative error δα_(t) and Expression (11) forthe absolute error Δα_(t) calculate the relative error and the absoluteerror between the input data Y_(t) and predicted value S1_(t) of thedata smoothing, respectively. In addition, Expression (14) for therelative error δγ_(t) and Expression (15) for the absolute error Δγ_(t)calculate the relative error and the absolute error between the gradient(S1_(t)−S1_(t-1)) of the predicted value of the data smoothing and thepredicted value B_(t) of the gradient of the smoothed data.

FIG. 8 shows a relation between a response coefficient and the absolutevalue of relative error/absolute error in a second embodiment of thepresent invention when an exponentiation N is used as a parameter. Theabsolute value of relative error/absolute error can evaluate adifference between the input data and the predicted value of the datasmoothing within a range of a maximum value of one to a minimum value ofzero. If the absolute value of relative error/absolute error is zero,the input data and the predicted value of the data smoothing match. Asshown in FIG. 8, when N=0, the response coefficient of the smoothingparameter is one, and a smoothing parameter becomes constant, which isthe same as the first embodiment of the present invention.

When N=1, the response coefficient increases from zero to one inproportion to the absolute value of the relative error/absolute error,and thus the smoothing parameter similarly increases from a minimumvalue to a maximum value. When N=5, the response coefficient increasesfrom zero to one with the fifth power of the absolute value of therelative error/absolute error, and thus the smoothing parametersimilarly increases from a minimum value to a maximum value with aresponsiveness of the fifth power. That is, as compared between thecases of N=1 and N=5, the smoothing parameter of the case of N=5 hasproperties of remaining smaller even if the input data somewhat differsfrom the predicted value of the data smoothing, and in contrast, ofsharply increasing the smoothing parameter when the input data largelydiffers from the predicted value of the data smoothing.

If the smoothing parameter is small, the S/N ratio of the dataprocessing increases but the absolute error increases, which makes theretardation time longer. On the other hand, if the smoothing parameteris large, the absolute error decreases and the retardation time is madeshorter, but the S/N ratio of the data processing decreases. It istherefore needed to select an optimal smoothing parameter in accordancewith the input data. The smoothing parameters are fixed in the firstembodiment of the present invention, but in the second embodiment of thepresent invention, the smoothing parameters are adjusted sequentially inaccordance with the difference between the input data and the predictedvalue of the data smoothing. For this reason, it is possible to avoidingthe tradeoff between the S/N ratio of the data processing, and theabsolute error and the retardation time, and to perform the datasmoothing process and the data differential process with a high S/Nratio, a small absolute error, and a short retardation time.

Furthermore, the smoothing parameter is changed sequentially inaccordance with the error between the input data and the predicted valueof the data smoothing, or the like, but once the smoothing parameterbecomes zero, the smoothing parameter is not changed thereafter. Inaddition, since the absolute error is made larger and the retardationtime is made longer when the smoothing parameter is close to zero,setting a lower limit value of the smoothing parameter within a variablerange has an advantage of performing a stable and optimal dataprocessing in an adaptive double exponential smoothing process.

FIGS. 9A-C show the data processing results when the exponentialparameter N=1 in the data smoothing process and the data differentialprocess device of the second embodiment of the present invention. FIG.9A shows input data and a waveform after data smoothing process, FIG. 9Bshows a waveform after the first differential process, and FIG. 9C showsa waveform after the second differential process. In addition, FIGS.10A-C shows the data processing results when the exponential parameterN=5 in the data processing apparatus of the second embodiment of thepresent invention. FIG. 10A shows input data and a waveform after datasmoothing process, FIG. 10B shows a waveform after the firstdifferential process, and FIG. 10C shows a waveform of a seconddifferential process. Here, the pieces of input data used for FIGS. 9A-Cand FIGS. 10A-C are the same as those for FIGS. 6A-C and FIGS. 7A-C.

As compared between FIGS. 9A-C and FIGS. 6A-C, with the data processingapparatus of the second embodiment of the present invention, when theexponential parameter N=1, as shown in FIG. 9B and FIG. 9C, the firstdifferential process and the second differential process can beperformed with a higher S/N ratio than the case of the first embodimentof the present invention. In addition, as compared between FIGS. 9A-Cand FIGS. 10A-C, with the data processing apparatus of the secondembodiment of the present invention, when the exponential parameter N=5,as shown in FIG. 10B and FIG. 10C, the first differential process andthe second differential process can be performed with an even higher S/Nratio than the case where the exponential parameter N=1.

Comparing data processing performance using numerical data, the absoluteerror is 23.6 by the data smoothing process and the data differentialprocess device of the second embodiment of the present invention whenthe exponential parameter N=1, whereas being 27.6 when the exponentialparameter N=5. Furthermore, the S/N ratio is 226.5 when the exponentialparameter N=1, whereas being 1607.2 when the exponential parameter N=5.The zero crossing time point in the second differential when theexponential parameter N=5 is earlier by 0.4 second than that when theexponential parameter N=1, which means that the retardation time isshort. As a result, it is possible to optimally select the exponentialparameter N and perform a desired data smoothing process and datadifferential process according to the degree of priorities among a highS/N ratio, an absolute error, and a retardation time in the dataprocessing performances.

FIGS. 11A-C show the data processing results in the case where achanging point follows immediately after the start of data input whenthe exponential parameter N=1 in the data processing apparatus of thesecond embodiment of the present invention. The result of data smoothingprocess, the result of first differential process, and the result ofsecond differential process are satisfactorily output based on the dataimmediately following the start of data input without lacking and with asmall error even if a changing point of the data follows immediatelyafter the start of the data input.

For this reason, the data processing apparatus of the second embodimentof the present invention is particularly useful for detecting the endpoint of etching process in a short-time etching process. Insemiconductor etching, along with higher integration and finergeometries for semiconductor devices, there are increased steps ofetching a multilayer thin film, and it is thus important to detect theend point of etching process in a short-time etching process or etchingstep. Deriving the predicted value of the data smoothing and thepredicted value of the gradient of the smoothed data immediatelypreceding the start of data input using the approximate polynomialdescribed with reference to FIG. 3 in the first embodiment of thepresent invention and setting them as initial values significantlycontributes toward supporting the short-time process. In additionthereto, with the second embodiment of the present invention, the S/Nratio is improved in the first differential process and the seconddifferential process, which allows for determining the end point ofetching process even more clearly.

In the case of the present embodiment, in addition to the advantage ofthe first embodiment, it is possible to perform the data smoothingprocess and the data differential process with a high S/N ratio,overcoming the tradeoff relationship between the S/N ratio, and theerror of absolute value and the retardation time, being the dataprocessing performances, since the smoothing parameter is optimizedsequentially in accordance with the error between the input data and thepredicted value of the data smoothing, or the like. For this reason,there is an advantage of controlling a target system (devices or thelike) with high precision since the state or the changes in the state inthe target system (devices or the like) can be clearly detected.

Third Embodiment

A data processing apparatus 1 according to a third embodiment of thepresent invention will be next described with reference to FIG. 12. Inthe present embodiment, Expressions (1) and (2) of the first-time doubleexponential smoothing process, in FIG. 2 showing the total flow of themethod of the data smoothing process and the data differential processin the first embodiment the present invention, are replaced with thefollowing Expressions (16) to (18) of a triple exponential smoothingprocess.Predicted value of the data smoothing:S1_(t)=α1Y1_(t)+(1−a1)(S1_(t)−1+B1_(t-1))  Expression (16)Predicted value of the gradient of the smoothed data: B1_(t)=γ1(S1_(t)−S1_(t-1))+(1−γ1)(B1_(t-1) +G1_(t-1)  Expression (17)Predicted value of the gradient of the gradient of the smoothed data:G1_(t)=β1(B1_(t) −B1_(t-1))+(1−β1)G1_(t-1)  Expression (18)

Next, a second-time double exponential smoothing process is performedtwice, in which the predicted value B1_(t) of the gradient of thesmoothed data of the first output is set as a second input data Y2_(t),and a predicted value G1_(t) of the gradient of the gradient of thesmoothed data in the first output is set as a second input data Y3_(t).Two predicted values S2_(t) and S3_(t) of the data smoothing in thesecond output are thereby obtained. Next, result data on the datasmoothing process S1_(t), result data on a first differential dataprocess S2_(t), result data on second differential data process S3_(t)are output collectively or sequentially.

Here, a smoothing parameter α1 of the predicted value of the datasmoothing, a smoothing parameter γ1 of the predicted value of thegradient of the smoothed data, and a smoothing parameter β1 of thepredicted value of the gradient of the gradient of the smoothed data inthe first-time triple exponential smoothing, and smoothing parameters α2and α3 of the predicted value of the data smoothing, and smoothingparameters γ2 and γ3 of the predicted value of the gradient of thesmoothed data in the second twice-performed double exponential smoothingare set in advance. Note that, 0<α1<1, 0<γ1<1, 0<β1<1, 0<α2<1, 0<γ2<1,0<α3<1, and 0<γ3<1.

The predicted value B1_(t) of the gradient of the smoothed data in thefirst output and the predicted value G1_(t) of the gradient of thegradient of the smoothed data in the first output may be used since thepredicted value B1_(t) is equivalent to the processing result of firstdifferential and the predicted value G1_(t) is equivalent to the resultof the second differential process, but the data results thereof varywidely, and thus the data smoothing process is performed by performingthe second-time double exponential smoothing process twice.

The smoothing parameters are fixed in the present embodiment, but aswith the second embodiment of the present invention, an adaptive tripleexponential smoothing process may be used in which the smoothingparameters are changed sequentially in accordance with the errorsbetween the input data and the predicted value of the data smoothing.

In the present embodiment, there is a function and an advantage similarto those of the first embodiment. In addition, the data smoothingprocess, the first differential process, and the second differentialprocess may be performed only by the first-time triple exponentialsmoothing process. In this case, there is an advantage that the datasmoothing process, the first differential process, the seconddifferential process can be simply performed in one process with a smalldata storage capacity. In addition, as can be easily inferred, by amethod similar to that of the present embodiment, expanding Expressions(16) to (18) to an N-tuple exponential smoothing process, can performthe data smoothing process and differential processes from the firstdifferential process to a (N−1)th differential process.

In the above-described embodiments, there have been described the caseswhere the data processing method and the data processing apparatus ofthe present invention are applied to the detection of the end point ofetching process in the microwave plasma etching, performing the etchingwith high precision, and there is an advantage that a target device canbe controlled with high precision also in etching devices orfilm-forming devices using other plasma production methods (inductivelycoupled method, parallel plate method, and the like), or processingapparatuses in other fields, or other devices, because using numericaldata obtained from the device or the like as an input and applying thedata processing apparatus and the data processing method of the presentinvention allows for monitoring the state of the device and detecting achanging point of the state with high precision.

In addition, there is an advantage that the data processing apparatusand the data processing method of the present invention can be appliedto economic field or financial field such as supply and demandestimation, so as to analyze data with high precision.

In the present invention, by the sequential data processing, the datasmoothing process and the data differential process can be performedwith a high S/N ratio, a small data delay, and high reliability even inan initial period of starting the data processing. In addition, with thepresent invention, a data smoothing value, a first differential value,and a second differential value can be sequentially obtained in realtime with a high S/N ratio, a short retardation time, or highreliability even in an initial period of starting the data processing.Furthermore, with the present invention, the target system can becontrolled with high precision using the data smoothing value, the firstdifferential value, and the second differential value.

Note that the present invention is not limited to the above-describedembodiments, but includes various modifications. For example, theabove-described embodiments have been described in detail such that thepresent invention is explained in an easily understandable manner. Thepresent invention is not limited to those having all the describedconfigurations. Part of the configuration of some embodiment may bereplaced with the configuration of other embodiments, or theconfiguration of the other embodiment may be added to the configurationof some embodiment. Furthermore, other configurations may be added to,delete from, or replaced with part of the configurations of eachembodiment.

It should be further understood by those skilled in the art thatalthough the foregoing description has been made on embodiments of theinvention, the invention is not limited thereto and various changes andmodifications may be made without departing from the spirit of theinvention and the scope of the appended claims.

The invention claimed is:
 1. A data processing apparatus comprising: aprocessing chamber in which a sample is subjected to an etching process;a measuring device which is configured to obtain data relating to theprocessing chamber; a first storage which is configured to store thedata received by the input/output device; a second storage which isconfigured to store a data processing program that includes the stepsof: calculating, using a double exponential smoothing method in whichthe data is set as an input value, a first predicted value that is apredicted value of smoothed data and a second predicted value that is apredicted value of a gradient of the smoothed data, as an output value;and calculating, using a double exponential smoothing method in whichthe second predicted value calculated as the output value is set asinput data, a third predicted value that is a predicted value ofsmoothed data and a fourth predicted value that is a predicted value ofa gradient of the smoothed data, as an output value; and a calculationprocessing apparatus which is configured to perform the data processingunder the data processing program; and a controller which is configuredto detect a state of the processing chamber or a change in the state ofthe processing chamber on the basis of the first predicted valuecalculated by the calculation processing apparatus as a result of a datasmoothing process, the second predicted value calculated by thecalculation processing apparatus or the third predicted value calculatedby the calculation processing apparatus as a result of a firstdifferential process, and the fourth predicted value calculated by thecalculation processing apparatus as a result of a second differentialprocess, respectively, wherein the controller is further configured todetect an end point of the etching process based on the detected stateor change in state of the processing chamber and to control theprocessing chamber in accordance with the detected end point.
 2. Aprocessing apparatus comprising: a processing chamber to be a controlobject and configured to perform an etching process; a measuring devicewhich is configured to obtain data relating to the processing chamber; acalculation processing apparatus which is configured to perform dataprocessing under a data processing program that includes the steps of:calculating, using a double exponential smoothing method in which thedata relating to the processing chamber is set as an input value, afirst predicted value that is a predicted value of smoothed data and asecond predicted value that is a predicted value of a gradient of thesmoothed data, as an output value; and calculating, using a doubleexponential smoothing method in which the second predicted valuecalculated as an output value is set as input data, a third predictedvalue that is a predicted value of smoothed data and a fourth predictedvalue that is a predicted value of a gradient of the smoothed data, asan output value; and a controller which is configured to detect a stateof the processing chamber or a change in the state of the processingchamber on the basis of at least one of the first predicted valuecalculated by the calculation processing apparatus, the second predictedvalue calculated by the calculation processing apparatus, the thirdpredicted value calculated by the calculation processing apparatus, andthe fourth predicted value calculated by the calculation processingapparatus, wherein the controller is further configured to detect an endpoint of the plasma etching process based on the detected state orchange in state of the processing chamber and to control the processingchamber in accordance with the detected end point.
 3. The processingapparatus according to claim 2, wherein the processing chamber is aprocessing chamber in which a sample mounted on a sample stage issubject to a plasma etching process.
 4. A processing apparatuscomprising: a processing chamber to be a control object and configuredto perform an etching process; a measuring device which is configured toobtain data relating to the processing chamber; a calculation processingapparatus which is configured to perform a processing of the data undera data processing program that uses a responsive double exponentialsmoothing method to generate a result of a data smoothing process thatis a first predicted value of smoothed data, a result of a firstdifferential process that is a second predicted value of a gradient ofthe smoothed data or a third predicted value of smoothed data, and aresult of a second differential process that is a fourth predicted valueof a gradient of the smoothed data, in which smoothing parameters arevaried based on an error between the data obtained by the measuringdevice and a predicted value of smoothed data, and that processes thedata while making a lower limit value of a variable range of thesmoothing parameters greater than zero; and a controller which isconfigured to detect a plasma processing state of the sample or a changein the plasma processing state of the sample on the basis of at leastone of the result of the data smoothing process calculated by theprocessing of the data, the result of the first differential processcalculated by the processing of the data, or the result of the seconddifferential process calculated by the processing of the data, whereinthe controller is further configured to detect an end point of theplasma etching process based on the detected plasma processing state orchange in plasma processing state of the sample and to control theplasma etching process in accordance with the detected end point.
 5. Aprocessing apparatus comprising: a processing chamber in which a samplemounted on a sample stage is subjected to a plasma etching process; ameasuring device which is configured to obtain light emission data inthe plasma etching process of the sample; a calculation processingapparatus which is configured to perform a processing of the data undera data processing program that uses a responsive double exponentialsmoothing method to generate a result of a data smoothing process thatis a first predicted value of smoothed data, a result of a firstdifferential process that is a second predicted value of a gradient ofthe smoothed data or a third predicted value of smoothed data, and aresult of a second differential process that is a fourth predicted valueof a gradient of the smoothed data, in which smoothing parameters arevaried based on an error between the data obtained by the measuringdevice and a predicted value of smoothed data, and that processes thedata while making a lower limit value of the variable range of thesmoothing parameters greater than zero; and a controller which isconfigured to detect a plasma processing state of the sample or a changein the plasma processing state of the sample on the basis of at leastone of the result of the data smoothing process calculated by theprocessing of the data, the result of the first differential processcalculated by the processing of the data, or the result of the seconddifferential process calculated by the processing of the data, whereinthe controller is further configured to detect an end point of theplasma etching process based on the detected plasma processing state orchange in plasma processing state of the sample and to control theplasma etching process in accordance with the detected end point.